Tony Abbott has told Chinese President Xi Jinping that China's growth and strength was "a benefit to the world, not a challenge".

And Mr Xi said that, in a phone call between the two men after Mr Abbott's election, "we reached a lot of agreement during that conversation".

The pair were meeting on the sidelines of the APEC summit in Bali late on Sunday night — Mr Abbott's first and in some ways most important bilateral encounter during this week's talks.

During opening remarks, Mr Xi congratulated Mr Abbott on his election, and said he appreciated the Prime Minister's "positive attitude" on growing the China-Australia relationship.

"I also firmly believe that as important countries in the Asia Pacific region, China and Australia entering into closer cooperation not only serves the interests of both our countries but will also add positive energy to the region," Mr Xi said.

He added that China was "ready to work with Australia to continue to substantiate China and Australia's strategic partnership".

Mr Abbott responded that it was an "honour" to meet Mr Xi, a man who has "seen more of Australia than many Australians".

"We have a strong relationship and it's my fervent hope it will become even stronger in the months and years ahead," Mr Abbott said.

He said Australians owed "much of our prosperity to the rapidly growing trade relations between our two countries". During the meeting, Mr Xi invited Mr Abbott for an official visit to China next year, and the Prime Minister accepted, saying he would bring with him a large delegation of business, trade and government representatives including State Premiers. Mr Abbott said he hoped to make the trip in the first half of next year. The Prime Minister and the Chinese president both expressed their strong commitment to accelerating Free Trade Agreement negotiations between the two countries. Mr Abbott said he was committed to further growing the relationship between Australia and China, not just through economic links, but cultural, scientific and academic as well.

After opening remarks, the conversation was closed and the media excluded.